# Multiresolution Deep Implicit Functions for 3D Shape Representation

arXiv: https://arxiv.org/abs/2109.05591 · HTML: https://mlsanity.com/paper/2109.05591/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 41 references that are in the map.
- First posted on arXiv 12 Sep 2021.

## Builds on (most cited first, 26 of 26)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization](https://mlsanity.com/paper/1912.07109/) (2019)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [Deep Level Sets: Implicit Surface Representations for 3D Shape Inference](https://mlsanity.com/paper/1901.06802/) (2019)
- [O-CNN: Octree-based Convolutional Neural Networks for 3D Shape Analysis](https://mlsanity.com/paper/1712.01537/) (2017)
- [Adversarial Generation of Continuous Implicit Shape Representations](https://mlsanity.com/paper/2002.00349/) (2020)
- [OctNetFusion: Learning Depth Fusion from Data](https://mlsanity.com/paper/1704.01047/) (2017)
- [Deep Octree-based CNNs with Output-Guided Skip Connections for 3D Shape and Scene Completion](https://mlsanity.com/paper/2006.03762/) (2020)
- [Deep Implicit Volume Compression](https://mlsanity.com/paper/2005.08877/) (2020)

## Built on by (most cited first, 30 of 35)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2209.08725/) (2022)
- [ShapeFormer: Transformer-based Shape Completion via Sparse Representation](https://mlsanity.com/paper/2201.10326/) (2022)
- [Grid-guided Neural Radiance Fields for Large Urban Scenes](https://mlsanity.com/paper/2303.14001/) (2023)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)
- [Towards Implicit Text-Guided 3D Shape Generation](https://mlsanity.com/paper/2203.14622/) (2022)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [Ponder: Point Cloud Pre-training via Neural Rendering](https://mlsanity.com/paper/2301.00157/) (2022)
- [Learning Deep Implicit Functions for 3D Shapes with Dynamic Code Clouds](https://mlsanity.com/paper/2203.14048/) (2022)
- [Controllable Mesh Generation Through Sparse Latent Point Diffusion Models](https://mlsanity.com/paper/2303.07938/) (2023)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation, Inversion, and Manipulation](https://mlsanity.com/paper/2302.00190/) (2023)
- [PatchComplete: Learning Multi-Resolution Patch Priors for 3D Shape Completion on Unseen Categories](https://mlsanity.com/paper/2206.04916/) (2022)
- [PINs: Progressive Implicit Networks for Multi-Scale Neural Representations](https://mlsanity.com/paper/2202.04713/) (2022)
- [PRIF: Primary Ray-based Implicit Function](https://mlsanity.com/paper/2208.06143/) (2022)
- [T2TD: Text-3D Generation Model based on Prior Knowledge Guidance](https://mlsanity.com/paper/2305.15753/) (2023)
- [An Implicit Parametric Morphable Dental Model](https://mlsanity.com/paper/2211.11402/) (2022)
- [RayDF: Neural Ray-surface Distance Fields with Multi-view Consistency](https://mlsanity.com/paper/2310.19629/) (2023)
- [ARMesh: Autoregressive Mesh Generation via Next-Level-of-Detail Prediction](https://mlsanity.com/paper/2509.20824/) (2025)
- [PatchRD: Detail-Preserving Shape Completion by Learning Patch Retrieval and Deformation](https://mlsanity.com/paper/2207.11790/) (2022)
- [OReX: Object Reconstruction from Planar Cross-sections Using Neural Fields](https://mlsanity.com/paper/2211.12886/) (2022)
- [GridFormer: Point-Grid Transformer for Surface Reconstruction](https://mlsanity.com/paper/2401.02292/) (2024)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [End-to-End Implicit Neural Representations for Classification](https://mlsanity.com/paper/2503.18123/) (2025)
- [DeepJoin: Learning a Joint Occupancy, Signed Distance, and Normal Field Function for Shape Repair](https://mlsanity.com/paper/2211.12400/) (2022)
- [Towards Croppable Implicit Neural Representations](https://mlsanity.com/paper/2409.19472/) (2024)
- [UNIST: Unpaired Neural Implicit Shape Translation Network](https://mlsanity.com/paper/2112.05381/) (2021)
- [Adaptive Local Basis Functions for Shape Completion](https://mlsanity.com/paper/2307.08348/) (2023)
- [Progressive Multi-scale Light Field Networks](https://mlsanity.com/paper/2208.06710/) (2022)

## Abstract (arXiv)

We introduce Multiresolution Deep Implicit Functions (MDIF), a hierarchical representation that can recover fine geometry detail, while being able to perform global operations such as shape completion. Our model represents a complex 3D shape with a hierarchy of latent grids, which can be decoded into different levels of detail and also achieve better accuracy. For shape completion, we propose latent grid dropout to simulate partial data in the latent space and therefore defer the completing functionality to the decoder side. This along with our multires design significantly improves the shape completion quality under decoder-only latent optimization. To the best of our knowledge, MDIF is the first deep implicit function model that can at the same time (1) represent different levels of detail and allow progressive decoding; (2) support both encoder-decoder inference and decoder-only latent optimization, and fulfill multiple applications; (3) perform detailed decoder-only shape completion. Experiments demonstrate its superior performance against prior art in various 3D reconstruction tasks.